The tale starts with an unidentified body found on the roadside. Hit by a car in the wee hours of the morning, investigators puzzled over where it had come from and how it had reached its asphalt resting place.

But this wasn’t a human murder mystery: The victim was a young cougar, struck down on the Wilbur Cross Parkway in Milford, Conn., on June 11. The incident shocked a state where drivers are accustomed to seeing white-tailed deer dash in front of their windshields, not 140-pound predat...